Quantum Harmonic Oscillator
Time-dependent Schrödinger equation — coherent state dynamics
State n
3
Displacement x₀
2.0
Speed ×
1.0
Show potential
Show energy levels
Coherent state |α⟩ = Gaussian
wave packet displaced by x₀.
Re(ψ) in
blue
, |ψ|² in
green
V(x) = ½x² in
orange
E_n = ℏω(n + ½)
Coherent states oscillate
without spreading — the most
"classical" quantum states.